Question

Your best friend Frank just celebrated his 30th birthday and wants to start saving for his anticipated retirement. Frank plans to retire in 35 years and believes that he will have 20 good years of retirement and believes that if he can withdraw $90,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Frank for all scenarios presented below is 8% per year. This is an annual rate, review each individual question for more specifics on compounding periods per year. Because Frank is planning ahead, the first withdrawal will not take place until one year after he retires. he wants to make equal annual deposits into his account for his retirement fund.

We are now back to Frank staring his retirement investments one year from now (35 years to retirement). Suppose Frank's employer will contribute $2,000 to the account each year as part of the company's profit sharing plan. In addition, assume that Frank has a trust fund that will pay out $25,000 to him when he is 50 (20 years from now). What amount must he deposit annually under these assumptions to be able to make the desired withdrawals at retirement?                   

To find the amount of the annual deposit now, it is easier to break down the components of the problem. Doing so for each of the following to find your friend's annual deposit, we get:

D1) Value of employer's contribution at retirement :

D2) Value of trust fund at retirement :

D3) Remaining amount that Frank needs at retirement:

D4) (Final answer) Amount to save each year under these assumptions

Answer 1

Amount required on the day of retirement is equal to the present value of future withdrawals

= 90,000*PVAF(8%, 20 years)

= 90,000*9.818

= $883,620

Value of employer's contribution at retirement = 2,000[{(1.08)³⁵-1}/0.08] = $344,633.61

Value of trust fund at retirement = 25,000(1+8%)¹⁵ = $79,304.23

Remaining amount that Frank needs at retirement = 883,620-344,633.61 – 79,304.23

= $459,682.16

Let amount to save each year be x

X*[{(1+8%)³⁵-1}8%] = 459,682.16

172.3168X = 459,682.16

X = $2,667.66

Hence, amount to be saved each year = $2,667.66